Mobile Phase Effects in Packed Liquid Chromatography Columns SIR: The origin of the hand broadening mechanisms residing in the mobile phase of packed chromatographic columns has been the subject of much discussion and numei'ous attempts have been made to 0bta.n expressions dehcribirig these mechanisms. It has been clearly established (9,9) t h a t the measured d u e of the mobile phase plate height in gas chromatography cannot be caxplained in terms of eddy diffusion, longitudinal diffusion, and resistance to niass transfer in the inter- and intraparticle spaces only. The discrepancy between the observcd and calculated values of the plate height has been wcribed by Giddings (9) to intercahannel nonequivaleuce, whereas van I{erge, Haarhoff, and Pretorius ( 2 ) have attributed it to a wall effect. Giddings (9) has scggested that all of tlie term? arising .'ram radial nonequilibrium in the mobile phase, with the exception of the intraparticle term. ~ h o u l dbe coupled in parallel with a 1-elocity-independent, eddy-diffusion tj.pe term. I n a general form H:;fh = ZC,u
+ Z(l//.j
+ l/CjU)--l
(1)
\\-hen A , > > C,zc. The term A represent.: the velocity-independent (eddy diffusion) contribution and Cu is the term describing the resistance to mass transfer in the mobile phase. ffKfb denot'es the sum of the cont.ributions of the mobile phase band broadening effects, other than longitudinal diffusion, to the total plate height. The subscripts j and i refer, respectively, tjo those mobile nhase resistance processes which are a:iected by convectional movement of th,: solute molecules, and those which are .not. An attempt lias recent'])- been made t'o obtain information experimentally on the coupling mechanism, using gas chroniatographic columns, but the results were not conclusive (12). However, it \vas suggested t h a t coc pling mechanisms 5hould be observable in systems employing liquid carriers. As .t result, an experimental study has been undertaken to investigate this proposal and also to evaluate the various mobije phase contributions t'o the plate height.
To eimlplify the analysis of the mobile 1)hase processes. uncoated spherical g l a s beadi, of a dizmeter of either 0.0195 0.0005 em. 'x 0.045 i 0.001 cin., mere packed in1;o a brass tube, 50 em. long and 0.925-vm. i. d. n-Butyl alcohol, in 5.5-pl. samples, was injected by means of a micrometer syringe.
The inlet system LT as connected directly to the top of the column so that the syringe needle extended to just below the top of the packing. n-Heptane was used as the carrier and the liquid eluted from the column was passed through a dielectric constant detector (16). The sensing cell of the detector consisted of two parallel perforated plates, of which the top plate was in direct contact with the bottom of the column packing. The volume between the plates was approximately 0.017 cu. cm. The cell formed part of an oscillator circuit and changes in the dielectric constant of the eluate were converted into voltage changes which were fed onto a recording potentiometer. The entire apparatus was thermostated a t 25.0' C.
h detailed study of additional sources of band broadening ( S ) , arising from noiiplug sample injection, detector volume, and sample volume, showed that these effects n-ere negligibly small in the apparatus described above. The random error associated with the observed plate height, measured by the peak-width-at-half-height method, was approximately 3y0. Experiments were carried out a t different flow velocities using the columnq described above and the total height equivalent per theoretical plate, H,n,b,which comprises contributions from all the mobile phase effects, wa5 deter-
14
L
u.cm sec-'
Figure 1 . Theoretical values of H,,, calculated from Equation 3, and experimental values of H',"fb for two particle diameters (a) HE$ ford, = 0.45 mm.
(b) (c)
(d)
H',":b for d, = 0.195 mm. H,, for d, = 0.45 mm. H V P for d, = 0.1 95 mm.
mined in each case. The interparticle linear flow velocity mas calculated from the volumetric flow rate, the i:ro>b sectionalarea of thecolumn, and the porosity of the packing. The values of Ihe porosity were determined by the method described by Anderson and Yapier (1) and were found to be 0.40 =t 0.01 for a n average particle diameter d, = 0.195 nim. and 0.43 =t0.01 for d, = 0.45 mm., which are in good agreement with the theoretically calculated value ( i ) . I n the system used here, H m o b contains contributions arising froni longitudinal diffusion of the solute, interparticle resistance to mass transfer, t h e mall effect and interchannel nonequivalence. The term describing the longitudinal diffuqion-Le.,
is well understood (8). I n Lqnatioii 2, u denotes the radial average of thc interparticle linear carrier flow velocity, D1 is the diffusion coefficient of t,hc solute in the mobile phase, and y i h a tortuosity factor. The v a l w of D1 was calculated b y the niet'hod of K l k c and Chang (17) and found to be (3.4 f 0.3) X 1 0 - 5 sq. cm.,;second. The consensus of various authors ( 2 , 5-7, 9, 15) is bhat the value of y is about 0.7 and a theoretically determined value of H l d can thereforr be confidently subt'racted from tlie csperimentally obserred H,,a value to isolate those band broadening nicchanisms which may be influenced by convect'ional movement of the solute molecules. Talues of the mobile phase plate height, Hg& determined in this way from the experimental result:, have been plotted in Figure 1 as a function of the linear flow velocity for tlie two particle diameters employed. From Figure 1 it is ,seen t,liat HE$ increases rapidly with flow velocity a t low values of u, and approaches a constant value a t higher flow rates. A similar result was obtained Ly Glueckauf ( I S ) . h striking feature of the curves in Figure 1 is that, HZtb is approximately proportional to dg at high flow velocities, while being at the same time essentially independent of u. Clearly none of t,he existing expreshions for mobile phase mass trawfer processes, which are of the forin ud;/ D1, can esplain this behavior unless witably modified. The contribution of int'erparticle resistance to mass transfer to HE$bmay be calculated from VOL. 35, NO. 10, SEPTEMBER 1963
1537
Table I. d, (inm.)
0 195 0 45
Experimental Values Calculated from Equations 6, 1 1 , and 12, Using the Data in Figure 1 rl X 1 0 3 (cni ) C (seconds) J@ 6 x 103 (Cm ) W x 0 24 i 0 0 2 0 86 f 0 01 2 GG i 0 113 1 9 f 0 2 34 i 0 .5 0 4 1 i 0 02 0 24 i 0 03 1 3.3 =!r 0 0.5 2 8 h 0 4 120 + 1 J 14 30 r!z 1 :3.3 0 41 =!r 0 0.3
u liere k 13 the ratio of tlie -tilute niabs in t h r stationary pha,e to that in the niotiile p1ia.e a t equilil~rinm and dl rrpre-ent> half the di\tance between two parallel plate5 in the general cl~roniatographicniodrl ( 10). -\ plot of Lquation 3 h a y bccw included in Figure 1, taking ( 2 ) d l = d,, 6, for d, = 0.45 mm. and 0.195 nini. Observation ,lie\\ that thc interparticle re-i-tance effect i- \ ery .mall in cornparimi n ith Hgtb. Moreover, the r u n e repre-eatthe ma\immn contriliution of H,, -inre, in practirc, it nil1 1)roIial)ly h a rccluc-ed a. a rc.ult of coupling n ith a velocit\--indri)endriit tcrni. The r u w i i - for tlii. art’ thc f o I l ( i ~ ing: \ Con-ider a cliaiincl t ) r t w e n nonlmrow ypherical 1)aic ~ c * l c ~in\ a I)ac.hed column. l‘lle diameter of -uch a c~lianiiclIS of the nrder of (1, 3 and t l i ~paraliolic flm velocity profile in the chsiitiel (10) may lie M ritten a5
\vliwe r is the distancr. from tlie center of the channel. -4 solute molecule can change its velocity by an amount I L hy diffusing a distance dn; 4x8 away from the surface of a [)article, in an average time of al)l)rosimately d i / 216D1. -1corres1)ondiiig rrsult may lie olhained for mass transfer by convection. The carrier velocity in a channel \vi11 change by an amount u in an average distance -d,,. -1tirile -d,,,u will therefore be required for the transport of a solute niolrcule by convectioii only, from the region near the surfaw of a particle to a rrgioii where the flobv velocity is equal to u . I t follo\vs tlicn that mass transfer h j - convection will have an alqireciable effert only on thv dif‘fusional processes in the intcriiarticlc s l i a w s \\.hen 11 ,‘s 216/)l,~d,. I f it is assumcd that 11, E lo-.: c ~ i iswond-’ .~ and d,, g 0.04 cm., it foilo1v.s that the, tliffusion:tl and convwtioiial I)rocrlsscs iviil comlwtr \vith ont’ anothrr a t f l o ~ vplocitics of -0.05 cni, sc~oiitl--’. Vrlociticr in this r q i o n ar(’ c~iiily at,tainable in pr:icticc sild it is clear that in chromatogra1)hic liquid carriw, the iiitrrlxirticle r(’sistance cor1trit)ution is of the. j-tyiw i l l Equation 1. To a good ai)i)rosimation, tht~r(~forc. th(x contritiutioli of H , , to Hrod mob can he ignored. The situation is sointvhat differrnt in gas chromstography, where D , G 0.1 c t ~ i .srcond-I. ~ 1538
0
ANALYTICAL CHEMISTRY
I n this caw, thc carricr gas velocity must be at least 500 cni. second-’ for convrction to affect the intrrimrticle resiitance tertii. Such high flow velocities do not occur in I)ract,ice and would, in any cast’, probably rrsult in turbulent f l ( ~ ~ v .Conscqucn t I y , in 1)rat t ice, the interparticle resistance term would h more convcnicntly dcscrihrd as a Citype term and should not be includd among thc j-tylw twnis, a:, pro1)ost~dby Giddings ( 0 ) . Thc variation of H g t b with flow vcllocity in Figuw I is cotisistertt, with a function of the gencral form ( 1 1 )
Sinw this r q ) r ( w n t s thr q u a t i o n of a straight line, of intercept 1;.L and graditwt 1,‘C, thr valws of . I and C can tir o h t a i n d l)y a linear rt>grcssioii analysis. The results are given in Table I , using t h r data in Figure 1. T w o niohilc phaw nirchanisnis have been formulatrd i n tcrnis of which t h r esl)erinirwtal data in Figure 1 may hr interl)rettv-the wall tffcct and interchannc.1 iionequivalrnc(.. The, most gmeral form of t h r cor,trihution of the \vaII rffwt to Hgt0 is givcn I)y
whi,re f i* a constant which i.: a nieasiir(> the iticrc1asv i n th(. carricr floiv velocity near tho wall of a ~ m c k r d coluniii, and 6’ is th(1 thickncw of thf. layc.r a t th(. column \\-all in units of d,,, ’l’hr radial diffusion coefficirnt. I],, niay tic1 tlefint~iin t m n s of thc total amount of soliitt~lwr unit volumc of thr c.olunin and t h r tots1 radial nia+ flus in tlw c~olunln. It follo\vs that (if
whrrc + 2 3 x cni. From ICquations 7 , 8, and 9, it is easily s w n that, for tht. present systrm,
sine(. k = 0. Exactly the same tls1)ression 1)-ould apply in gas liquid chromatography, sincc (D,)? I. The tistimatcd valurx- of j”0 ar? - ( ~ t i hat i ~ ymallcr than thc 1 aluc- rfportcid by van 13ergc et ul. 12); the value\ of + are i n fair agreenic.nt 111th that o h - r ~ c dby Hartman et a1 ( 1 4 ) . I11 tmii- of thc intrrc~haiinrl noiiequivalrwcc rffcct. thr (~-+rv--ion~for .I and C ma! he n r i t t w a-
arc prcwnt in packed columns, although their relative magnitudes cannot be estimated. Experiments which are desiqned to solve this problem could possilily 1~ carried out by eliminating the wall effect-e.g., by roughening thc column u-alIs--or by employing a Ixicking containing prrfectly uniform c.harinc3ls. ACKNOWLEDGMENT
1'. C. H., of the ;itomic Energy Board, c y r e s w s hi. thanks for permission t o 1iarticipato in this project. LlTERATURli CITED
1) Anderson, J. R.. Sapier, K. H., ~ u s t r c d z a nJ . CIzeni. 10,250 (1957). ( 2 ) Bcrge, P. C. var,, Haarhoff, P. C., Prrtorius, V., l'ranr. Faraday Soe. 58, 2272 ( 1962 1.
(
(3) Berge, P. C. van, Pretorius. T,, Pretoria University, Pretoria, South Africa, unpublished data, 1962. ( 4 ) Bohemen, J., Purnel!: J H., "Gas Chromatograph\. 1958, I). H. Ilrstv, ed.. D. 6. Buttemorths. London. IOFih. ( 5 ) Bihemen, J., Purnell, J. H., /. C'heni. SOC.1961, 360. (6) Ibzd., p. 2630 (7) Carman, P. C., "Flow
of
(iases
through Porous Media," 13. 45, Butterworth;, London. 1956. 18) ~, Deemter. J. J. van. Zuiderwcv. F. J.. Klinkenberg, -4.,Chri~l. Eng. "hi.5 ; 271 (1956). ( 9 ) Giddings, J. C., A s a ~ .C'im>i. 34, l l S 6 (106%). (10) (iiddinga, J. C., J . C'hroiiintog. 5 , 46 (1!)61). i l l ) Giddines. J. (1.. .Ycit~(r~184. 357 11959). ( 1 2 ) Giddings, J. C., Robison, R. A , A \ IL. CHEM.34, 885 (1962).
(13) Glueckauf, E., "T'apour Phase Chromatography," I). H. Destv, ed., p. 29, Buttrrworths, London, 19.57
(14) Hartman, AI. E., Revers, C. J. H., Kraniers, H., C h r m Eng. Sci. 9, 80 (1958). (15) Kieselbach, R., ANAL. CHEM. 33, 23 (1961). (16) Turner, I). 11- , Sature 181, 1265 f 1958). (17) Wilke, C. R , Chang, P , d.I.Ch.E J . 1, 261 (1955). s. hT. GOREON
G. J. KRIGE P. C. HAARHOFF VICTORPRETORICS
I>rJpt.of Physical anti Theoretical Chemistry University of Pretoria Pretoria, South Africa RECEIIEEL) for review January 8, 1963. Resubmitted March 18, 1963. Accepted Mav 6, 1963. S. RI G is indebted to the South African Atomic Energv Board, and G. J. K to the Council for Scientific and Industrial Rrse:irch. for the :\\\ard of bursaries.
Ina dve rtent Iso merizat io n of PoIy umaturated Acids Duiring Ester Preparation Highly un.aburatet1 fatty acidslinoleic. aciti-may be inadvertently iwiiierizcd (conjuga1:ed) during the ;irc'paration of esters for gar chromatography when the nicthod involve. a saponifiration step. Daniels and Richnond ( I ) have shown in a similar study that iwnierized 11oly.insaturated acids Iiave ,+ignificantiylonger retention time. than the parent acic Y and empliasizthc iniiiortance of Liqing mild condition. for the saponification of lipids containing s m h acids durinp; the preparation of fatty acid esters for gas chromatogral)hy. 'I'hc esters of isomerized linoleic acid have an emergent time almost identiral to that of the corre:yonding ester of Iinolcnic acid when chromatographed oil a conventional 'diethylene glycwl succinate Iwlyester :degs) gas chromatograph colmnn. Because of the possibility of niisintrm-pretation of the data as a result of this inadvertrnt isomerization. the following study va.: niade. Si11:
P.A.,
EXPERIMENTAL
'l'o demonhtrate that polyunsaturated acids of a glyceride c , m be easily isonierized during the preparation of esters for ga- chromatography. methyl eqterz n e r e prepared from saffloner oil as folio\\-. ' General Ester Preparation Procedure. Aibout 200 mg;.of sample n a s reactctl with about :L 50% eycesq of p o t a s i u m hydroxide ( K O H ) in ap-
proxiniatrly 2 nil. of anhydrou- mcthaiiol. The mixture was heated on a steaiii bath until the bulk of t h e alcohol n-a. removed. Ahout 0.25 nil. of ivater wan added, and t h r iniuturr TI traces of methanol. .lbout 2 ml. of viater was added and the iiotassium soaps w r e converted to acids i\-ith 4.Y aqueous HCI. The fatty acids were extracted with hexane. and the extracts were concentrated on a steam bath. The free fatty acids were disolved in ebhyl &her and converted to methyl esters with diazomethane. The ether was removed and the esters were stored under nitrogal until chromatographed. Preparation of Methyl Esters of Safflower Oil. I n the preparation of methyl ester sample S o . 1, the saponificat'ion and methanol removal st'cps. as n-cll as other solvent removal -'tc.ps. were prolonged. The s t q ) involving the removal of the bulk of tlir niet,hparticularly p r o l o n g d to about 45 minutes. The preparat,ion of methyl eater sanii)le S o . 2 was performed as rapidly as feasible. I n addition, the step involving the removal of the bulk of the mpthanol was controlled such t'hat alcohol reinoral prior to the addition of n-ater vias not complete. Conditions for the preparation of methyl ester sample S o . 3 were Fimilar to those used for sample No. 2 n.ith esceytion that' the solvent removal stcps were performed under a nitrogen atmosphere. The methyl ester sample S o . 3 was prepared from fatty acids derived from safflon-er oil ~-1iichwas isomerized in ethylene glycol-KOH reagent a t 180" C. for 2 hours.
The nicthyl e-tcr- were chroniatographed on a Barber-Colman Jlodel 20 argon ionization detector chromatograph, equipped with a &foot X 3/lsinch 0.d. column packed with 60- to 80-meah Chromosorb IT coated with 30% by weight of degs. The qamplcx chromatographed was 50 f i g . ; gas prebsure was 17 p.7.i.g.; column, detector. and flash heater temperature. wrre 193", 206', and 332" C., rey2ectively. RESULTS A N D DISCUSSION
The rewlt. of chromatography of the-e samples are \honn in TalAe I . The weight per cent compodions (not corrected for nonlincwity of rrq)on>e) nere determined b j the conventional triangulation method. Carhoii nunihers n ere determined by the conventional graphic procedure ( 3 ) . Sample 4 1- known, by the iwthod of preparation, to contain conjugated diene. The greatly diminished prak for .ample 1 a t carbon number 19.5 (linoleic acid) and the appearance of the large peak at carbon nunitier 20.6 drongly sugge-t that the latter reprerents conjugated diene. This indication 1'; supported by thc cloy agreement betn e m the iodine valuccalculated on thii as.umption nith t h r original R'ijs iodine value. This a
